the polynomial has the factor (x-n)
So any polynomial with these roots, must have the factors (x+sqrt(3))(x-sqrt(3))(x+2)
Since these are cubic polynomials (highest x term is x^3), these are all the factors, so the polynomial is of the form:
k(x+sqrt(3))(x-sqrt(3))(x+2)
And since the x^3 term is 1, the constant k must be 1.
So, the polynomial must be the one which is equal to:
(x+sqrt(3))(x-sqrt(3))(x+2)
Since the constant term (the last term) is different for each of your 4 options, you just need to evaluate the constant term and see which one matches.
i.e. the answer is whichever polynomial has a constant term equal to
sqrt(3) times (-sqrt(3)) times 2
